Correct Option: B
| (A + B)’s 1 day’s work = | 1 | |
18 |
| (B + C)’s 1 day’s work = | 1 | |
9 |
| (A + C)’s 1 day’s work = | 1 | |
12 |
Adding all the above three,
| 2 (A + B + C)’s 1 day’s work = | 1 | + | 1 | + | 1 |
18 | 9 | 12 |
| 2 (A + B + C)’s 1 day’s work = | 2 + 4 + 3 | |
36 |
| 2 (A + B + C)’s 1 day’s work = | 9 | = | 1 | |
36 | 4 |
| ∴ (A + B + C)’s 1 day’s work = | 1 | |
8 |
∴ B’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s work
| B’s 1 day’s work = | 1 | - | 1 | |
8 | 12 |
| B’s 1 day’s work = | 3 - 2 | = | 1 | |
24 | 24 |
Hence, B alone can do the work in 24 days.
Second method to solve this question ,Here , x = 18 , y = 9 , z = 12
| Time taken = | 2xyz | |
- xy + yz + zx |
| B alone can do in = | 2 × 18 × 9 × 12 | |
- 18 × 9 + 12 × 9 + 12 × 18 |
| B alone can do in = | 36 × 108 | |
- 162 + 108 + 216 |
| B alone can do in = | 36 × 108 | = 24 days |
162 |
